Restricting the preferences of the agents by assuming that their utility functions linearly depend on a payment allows for the positive results of the Vickrey auction and the VickreyClarke-Groves mechanism. These results, however, are limited to settings where there is some commonly desired commodity or numeraire—money, shells, beads, etcetera—which is commensurable with utility. We propose a generalization of the Vickrey auction that does not assume that the agents’ preferences are quasilinear, but nevertheless retains some of the Vickrey auction’s desirable properties. In this auction, a bid can be any alternative, rather than just a monetary offer. As a consequence, the auction is also applicable to situations where there is a fixed budget, or no numeraire is available at all (or it is undesirable to use payments for other reasons)—such as, for example, in the allocation of the task of contributing a module to an open-source project. We show that in two general settings...